Dynamics of Coastal Models - Manejo Costero

Hydraulic jumps 311R = 0.1η′10Branch 2F < 1Inflection pointBranch 3Branch 4Branch 1F = 1F > 1–10x1′1x ′ , η′0 0F < 1η′ = sx ′η′0F = 1Path(subcritical)F > 1–10 1x ′Figure 8.10 Both panels are plots of normalized surface elevation 0 against distance x 0 forR ¼ 0.5. The three branches of the solution are numbered 1, 2, and 3, and the constant-depthsolution, H 0 ¼ 1, is labeled as branch 4 and appears as a straight line (with slope 1).For the first solution represented by (8.68), (8.69), x 0 is a single-valued functionof H 0 .WhenH 0 is plotted as a function of x 0 , or equivalently, when 0 is plotted against x 0 ,the logarithmic divergence of f at H 0 ¼ 1 has the effect of producing three branches.Figure 8.10 contains a plot of 0 against x 0 for R ¼ 0.5. The three branches arenumbered 1, 2, and 3, respectively in the upper panel. These curves of 0 ðx 0 Þ correspondto the variation with x 0 of the ocean surface. The second, constant-depthsolution, H 0 ¼ 1, is labeled as branch 4 in the upper panel of Figure 8.10, and appearsas a straight line (with slope –1). Another straight line in Figure 8.10, also withslope –1, is labeled as F ¼ 1 in the upper panel and corresponds to